SPH3U · Exam review

Physics Exam Review

A practice exam with questions from all 6 units, then the key facts from every lesson, unit by unit. For a deeper look at one unit, open its test review.

Unit test reviews

Practice exam

36 questions, the same number from each unit. Each one shows the lesson it comes from.

Unit 1: Describing Motion: Scalars, Vectors and Measurement
1
A cyclist rides $3.0 km [N]$ , then $4.0 km [S]$ . What is the magnitude of the displacement?
Unit 1: Uniform Motion and Motion Graphs
2
A position-time graph is a horizontal line. What is the object doing?
Unit 1: Acceleration and the Kinematic Equations
3
A car speeds up from $10.0 m/s$ to $30.0 m/s$ in $5.00 s$ . What is its acceleration in $m/s^{2}$ ?
m/s^2
Unit 1: Acceleration and the Kinematic Equations
4
Order the steps for solving a kinematics problem reliably.
1. 1Check the sign and whether the size is physically plausible
2. 2Rearrange algebraically, then substitute the numbers
3. 3Pick the equation that is missing the blank variable
4. 4Draw the motion and choose a positive direction
5. 5List all five variables, marking the known, the wanted and the blank
Unit 1: Free Fall and Motion in Two Dimensions
5
Match each situation to the correct statement about it.
1. A.Acceleration zero, velocity constant
2. B.Crossing time unaffected, but swept downstream
3. C.Displacement zero, speed equal to launch speed
4. D.Velocity zero, acceleration still $9.81 m/s^{2}$ down
Object at the top of its flight
Skydiver at terminal velocity
Ball returning to its launch height
Boat aimed across a perpendicular current
Unit 1: Analysing Motion Data from an Experiment
6
Match each graph to the quantity its slope gives.
1. A.Acceleration, in $m/s^{2}$
2. B.Half the acceleration
3. C.Rate of change of acceleration — not used in this course
4. D.Velocity, in m/s
Position against time
Velocity against time
Position against time squared, from rest
Acceleration against time
Unit 2: Forces, Weight and Free-Body Diagrams
7
What is the weight, in newtons, of a $25 kg$ crate on Earth?
N
Unit 2: Newton's Three Laws of Motion
8
A net force of $84 N$ acts on a $12 kg$ object. What is its acceleration in $m/s^{2}$ ?
m/s^2
Unit 2: Net Force in One Dimension
9
Forces of $80 N$ right and $30 N$ left act on an object. What is the magnitude of the net force, in newtons?
N
Unit 2: Net Force in One Dimension
10
Match each lift situation to what the scale reads.
At rest
Accelerating upward
Accelerating downward
Cable cut, in free fall
Unit 2: Friction and the Coefficient of Friction
11
A box is pushed with $60 N$ and does not move. Maximum static friction is $75 N$ . What is the friction force acting?
Unit 2: Forces in Action: Air Resistance, Terminal Velocity and Safety
12
Match each safety feature to what it physically does.
Crumple zone
Airbag
Helmet foam liner
Gym mat
Unit 3: Work, Power and Efficiency
13
A force of $45 N$ pushes a box $12 m$ in the direction of the force. How much work is done, in joules?
J
Unit 3: Kinetic Energy, Potential Energy and Conservation
14
What is the kinetic energy, in joules, of a $4.0 kg$ object moving at $6.0 m/s$ ?
J
Unit 3: Thermal Energy, Heat Capacity and Phase Change
15
How much heat, in joules, is needed to raise $0.50 kg$ of water by $30^{\circ} C$ ? Take $c = 4180\ \text{J/{(kg}\cdot^\circ\text{C)}}$ .
J
Unit 3: Thermal Energy, Heat Capacity and Phase Change
16
Order the stages of taking ice at $- 10^{\circ} C$ to steam at $110^{\circ} C$ .
1. 1Warm the steam from $100^{\circ} C$ to $110^{\circ} C$
2. 2Boil the water at $100^{\circ} C$
3. 3Warm the water from $0^{\circ} C$ to $100^{\circ} C$
4. 4Warm the ice from $- 10^{\circ} C$ to $0^{\circ} C$
5. 5Melt the ice at $0^{\circ} C$
Unit 3: Nuclear Energy, Half-Life and Energy Sources
17
Order these isotopes from shortest half-life to longest.
1. 1Iodine-131 (8 days)
2. 2Plutonium-239 (24 100 years)
3. 3Cobalt-60 (5.27 years)
4. 4Technetium-99m (6 hours)
Unit 3: Thermal Energy in Buildings and the Environment
18
Match each building feature to the mechanism it is designed to fight.
Weatherstripping around a door
Glass-fibre batt in a wall cavity
Low-emissivity coating on glass
Argon fill between two panes
Unit 4: Wave Anatomy and the Wave Equation
19
A wave has frequency $40 Hz$ and wavelength $2.5 m$ . What is its speed, in m/s?
m/s
Unit 4: The Speed of Sound, Echoes and Mach Number
20
What is the speed of sound in air at $30^{\circ} C$ , in m/s?
m/s
Unit 4: Reflection, Superposition and Beats
21
Two tuning forks of $512 Hz$ and $518 Hz$ sound together. What is the beat frequency, in hertz?
Hz
Unit 4: Reflection, Superposition and Beats
22
A string is tuned against a $440 Hz$ fork. Order these beat frequencies from most in tune to least.
1. 11 beat per second
2. 29 beats per second
3. 35 beats per second
4. 40 beats per second
Unit 4: Resonance, Harmonics, Intensity and Hearing
23
Order these sounds from quietest to loudest.
1. 1Normal conversation ( $60 dB$ )
2. 2Jet engine close up ( $140 dB$ )
3. 3Power tools ( $100 dB$ )
4. 4Rustling leaves ( $20 dB$ )
Unit 4: Sound in Technology, Medicine and the Environment
24
Order these spaces from the shortest reverberation time to the longest.
1. 1Classroom with carpet, ceiling tile and people
2. 2Bare concrete-block gymnasium
3. 3Concert hall designed for orchestral music
4. 4Recording studio, heavily treated
Unit 5: Static Charge, Current and Electron Flow
25
A charge of $45 C$ flows past a point in $9.0 s$ . What is the current, in amperes?
A
Unit 5: Voltage, Resistance, Ohm's Law and Electrical Power
26
A $9.0 V$ battery drives $0.30 A$ through a resistor. What is its resistance, in ohms?
ohms
Unit 5: Series and Parallel Circuits
27
Resistors of $8.0 Ω$ , $12 Ω$ and $20 Ω$ are connected in series. What is the total resistance, in ohms?
ohms
Unit 5: Series and Parallel Circuits
28
Order the steps for analysing a circuit.
1. 1Find the total current from the supply voltage
2. 2Check that series voltages sum to the supply, or parallel currents to the total
3. 3Work back to find the voltage or current at each component
4. 4Find the total resistance using the appropriate combination rule
Unit 5: Magnetic Fields, Motors and Transformers
29
Order the stages electricity passes through from the generator to a household outlet.
1. 1Step-up transformer to $230$ – $500 kV$
2. 2Pole transformer steps down to $120/240 V$
3. 3Substation steps down to $27.6 kV$
4. 4Generator at about $20 kV$
Unit 5: Household Circuits, Safety and Static in Practice
30
A technician handles a memory module without a wrist strap and it fails afterwards. What most likely happened?
Unit 6: The SPH3U Formula Sheet, Decoded
31
Which of these formulas is not printed on the SPH3U formula sheet?
Unit 6: The SPH3U Formula Sheet, Decoded
32
In the transformer relationship, which ratio is inverted relative to the others?
Unit 6: The SPH3U Formula Sheet, Decoded
33
Order these strands as they appear on the SPH3U formula sheet.
1. 1Waves and Sound
2. 2Electricity and Electro Magnetism
3. 3Energy
4. 4Kinematic
5. 5Forces
Unit 6: How to Attack a Physics Problem
34
Which check would most quickly reveal that a household appliance 'draws $2400 A$ '?
Unit 6: How to Attack a Physics Problem
35
A question asks for a displacement and a student answers ' $14 m$ '. What is missing?
Unit 6: How to Attack a Physics Problem
36
Which of these does not limit the significant figures in an answer?

Key facts by unit

Unit 1: Kinematics

Describing Motion: Scalars, Vectors and Measurement

Displacement $Δ d = d_{f} - d_{i}$ is a vector and needs a direction. Distance is the scalar path length and has none.
Average speed uses total distance; average velocity uses displacement. They agree only for motion that never reverses.
Multiplying or dividing: keep the fewest significant figures. Adding or subtracting: keep the fewest decimal places.
Convert to base SI units before substituting. Divide km/h by $3.6$ to get m/s.
In one dimension a direction is a sign. Choose a positive direction, state it, and never change it mid-problem.
An answer with no unit — or a vector answer with no direction — is not finished.

Uniform Motion and Motion Graphs

Uniform motion means constant velocity: equal displacements in equal times, same direction throughout.
$v = \frac{Δ d}{Δ t}$ , rearranged as $Δ d = v Δ t$ or $Δ t = \frac{Δ d}{v}$ .
Slope of a position-time graph is velocity. Slope of a velocity-time graph is acceleration.
Area under a velocity-time graph is displacement; area below the axis counts as negative.
Slope of a chord gives average velocity; slope of a tangent gives instantaneous velocity.
A horizontal line on a $d$ - $t$ graph means at rest; a horizontal line on a $v$ - $t$ graph means constant velocity.

Acceleration and the Kinematic Equations

$a = \frac{Δ v}{Δ t} = \frac{v _{f} - v _{i}}{Δ t}$ , measured in $m/s^{2}$ .
Same signs on velocity and acceleration means speeding up; opposite signs means slowing down.
$v_{f} = v_{i} + a Δ t$ (no displacement) and $v_{f}^{2} = v_{i}^{2} + 2 a Δ d$ (no time).
$Δ d = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$ (no final velocity) and $Δ d = v_{f} Δ t - \frac{1}{2} a Δ t^{2}$ (no initial velocity).
Memorize the off-sheet one: $Δ d = (\frac{v _{i} + v _{f}}{2}) Δ t$ , which is missing acceleration.
These four equations are only valid while the acceleration stays constant. Split the problem at any point where it changes.

Free Fall and Motion in Two Dimensions

Free fall: $a = g = 9.81 m/s^{2}$ downward, the same for every mass, with air resistance ignored.
Taking up as positive makes $a = - 9.81 m/s^{2}$ ; taking down as positive makes it $+ 9.81 m/s^{2}$ . State which you chose.
At the top of a throw the velocity is zero but the acceleration is still $9.81 m/s^{2}$ downward.
An object returning to its launch height has $Δ d = 0$ and the same speed it left with.
Perpendicular vectors add by Pythagoras, $R = A^{2} + B^{2}$ , with the angle from $tan^{- 1}$ .
$[N 3 5^{\circ} E]$ starts at north and turns toward east — the first letter is the starting axis.
Relative velocity: $v_{object/ground} = v_{object/medium} + v_{medium/ground} .$

Analysing Motion Data from an Experiment

An interval velocity is $Δ d /Δ t$ across one timing interval, and it is plotted at the midpoint time of that interval.
A line of best fit is a single straight line drawn through the scatter — never a dot-to-dot, and never forced through the origin.
Take slope points from the drawn line, far apart, and divide the units as well as the numbers.
Slope of $d$ against $t$ is velocity (m/s); slope of $v$ against $t$ is acceleration ( $m/s^{2}$ ).
For an object starting from rest, plotting $d$ against $t^{2}$ straightens the curve and gives a slope of $\frac{1}{2} a$ .
Random errors scatter both ways and shrink when you average; systematic errors push one way and averaging never helps.
$% error = \frac{∣ measured - accepted ∣}{accepted} \times 100%,$ with the accepted value always on the bottom.

Unit 2: Forces

Forces, Weight and Free-Body Diagrams

A force is a push or pull measured in newtons, $1 N = 1 kg \cdot m/s^{2}$ , and it is always a vector.
$F_{g} = m g$ with $g = 9.81 m/s^{2} = 9.81 N/kg$ . Mass must be in kilograms.
Mass is matter in kilograms and does not change with location; weight is a force in newtons and does.
Normal means perpendicular to the surface — and $F_{N}$ is not automatically equal to the weight.
Tension is always a pull along the rope, away from the object.
A free-body diagram shows one isolated object and only the forces acting on it.

Newton's Three Laws of Motion

First law: with zero net force, an object keeps its velocity — at rest or moving in a straight line at constant speed.
Inertia is resistance to a change in velocity, and mass is its measure.
Second law: $F_{n e t} = m a$ . The acceleration points along the net force, not along any single force.
Zero net force means zero acceleration, which is the first law restated.
Third law: if A pushes B, B pushes A equally and oppositely. The two forces act on different objects.
Action-reaction pairs never cancel, because they never act on the same object.
Weight and normal force are not a third-law pair — same object, different force types.

Net Force in One Dimension

$Σ F = F_{n e t} = F_{+} + F_{-}$ — add the forces with their signs, after declaring a positive direction.
Balanced forces (net zero) mean equilibrium: at rest or moving at constant velocity.
Unbalanced forces produce acceleration in the direction of the net force, with $F_{n e t} = m a$ .
A scale reads the normal force, not the weight. They differ whenever there is vertical acceleration.
Accelerating upward makes you feel heavier; accelerating downward makes you feel lighter; free fall gives $F_{N} = 0$ .
Connected objects share one acceleration. Find it with the system approach, then get tension from one object alone.
In an ideal rope the tension is the same throughout, and an ideal pulley only redirects it.

Friction and the Coefficient of Friction

Friction opposes relative sliding between surfaces and always acts along the surface.
$μ = \frac{F _{f r i c t i o n}}{F _{n or ma l}}$ , so $F_{f r i c t i o n} = μ F_{n or ma l}$ . It is a ratio, so it has no units.
Static friction adjusts to match the applied force up to a maximum; kinetic friction is constant and lower.
$μ_{s t a t i c} > μ_{kin e t i c}$ , which is why an object lurches as it breaks free.
Friction depends on the surface pair and the normal force — not on the apparent contact area.
On level ground with no extra vertical force, $F_{N} = m g$ .
The coefficient describes two surfaces together, never one material alone.

Forces in Action: Air Resistance, Terminal Velocity and Safety

Air resistance opposes motion through the air and grows as the object speeds up; it also grows with frontal area and with a less streamlined shape.
As a falling object speeds up, drag grows, the net force shrinks and the acceleration shrinks — the object is still speeding up, just more slowly.
Terminal velocity is reached when drag exactly balances weight: net force zero, acceleration zero, velocity constant and large.
Opening a parachute multiplies the drag, so the net force points upward while the motion is still downward — rapid slowing to a new, far lower terminal velocity.
A feather and a hammer fall together only in a vacuum; in air the feather's huge area-to-mass ratio gives it a tiny terminal velocity.
In a collision the change in velocity is fixed. Extending the stopping time reduces the acceleration, and $F_{n e t} = m a$ then reduces the force by the same factor.
Crumple zones, airbags, helmets and padded surfaces all work the same way: they make the stop take longer.

Unit 3: Energy and Society

Work, Power and Efficiency

$W = F d cos θ$ , measured in joules. Work is a scalar even though force and displacement are vectors.
A force perpendicular to the displacement does zero work — carrying a box across a level room is the standard case.
Negative work removes energy: friction, braking and lowering a load all do negative work.
$Σ W = W_{n e t} = W_{+} + W_{-}$ .
$P = \frac{W}{Δ t}$ , in watts, where $1 W = 1 J/s$ . Not on the formula sheet.
$efficiency = \frac{E _{u se f u l}}{E _{t o t a l}} \times 100% .$ Not on the formula sheet.
The 'lost' energy in an inefficient device is almost always thermal energy dispersed into the surroundings.

Kinetic Energy, Potential Energy and Conservation

$K E = \frac{1}{2} m v^{2}$ — doubling the speed quadruples the kinetic energy.
Kinetic energy is a scalar and is never negative, because the velocity is squared.
$PE = m g h$ , where $h$ is the vertical height above a reference level you choose and state.
Energy is never created or destroyed, only transformed or transferred.
Without friction, $K E_{i} + P E_{i} = K E_{f} + P E_{f}$ — mechanical energy is conserved.
With friction, the missing mechanical energy has become thermal energy: $K E_{i} + P E_{i} = K E_{f} + P E_{f} + E_{t h er ma l} .$
Energy methods ignore the path, which is what makes them work where kinematics cannot.

Thermal Energy, Heat Capacity and Phase Change

Temperature is average particle kinetic energy; thermal energy is the total; heat is thermal energy in transit.
Heat moves by conduction, convection and radiation — only radiation works through a vacuum.
$Q = m c Δ T$ for a temperature change, with $Δ T$ as final minus initial.
Water's specific heat is $4180\ \text{J/{(kg}\cdot^\circ\text{C)}}$ — unusually high, which is why it is a good coolant.
$Q_{re l e a se d} + Q_{ab sor b e d} = 0$ when two objects reach a common final temperature.
$Q = m L_{f}$ to melt or freeze, $Q = m L_{v}$ to boil or condense. Neither contains $Δ T$ .
For water, $L_{f} = 3.34 \times 1 0^{5} J/kg$ and $L_{v} = 2.26 \times 1 0^{6} J/kg$ .
During a phase change, temperature does not rise even though energy is being added.

Nuclear Energy, Half-Life and Energy Sources

Fission splits a heavy nucleus and drives every commercial reactor; fusion joins light nuclei and powers stars.
Ontario's CANDU reactors use heavy water, run on unenriched uranium, and can be refuelled while operating.
Half-life is the time for half the nuclei in a sample to decay. It is fixed for each isotope.
$A = A_{0} (\frac{1}{2})^{t / h}$ — use the same time unit for $t$ and $h$ .
Each half-life removes half of what remains: after three, one eighth is left, not zero.
Ontario's electricity is roughly 50–60% nuclear and about 25% hydroelectric, with coal phased out in 2014.
Wind and solar are intermittent, so a grid relying on them needs storage or dispatchable backup.

Thermal Energy in Buildings and the Environment

Air leakage is usually the single largest heat-loss path in an older house, ahead of walls, roof, windows and basement.
Insulation works by trapping still air in pockets small enough to stop convection currents forming.
R-value measures resistance to heat flow, so a larger value means slower loss, and the layers in an assembly add.
Heat escapes by the path of least resistance, so the weakest element sets the loss — upgrade that one first.
Double glazing blocks conduction with a low-conductivity gas, convection with a narrow gap, and radiation with a low-emissivity coating.
Thermal mass is a large $m c$ product, so $Q = m c Δ T$ gives a small $Δ T$ for a large $Q$ . It flattens temperature swings; it does not reduce the total heat flow.
A heat pump moves existing thermal energy rather than generating it, so its coefficient of performance — heat delivered over electricity used — is typically 2 to 4.
$1 kWh = 3.6 \times 1 0^{6} J$ , the unit electricity is billed in.

Unit 4: Waves and Sound

Wave Anatomy and the Wave Equation

A wave transfers energy without transferring matter.
Transverse waves vibrate perpendicular to travel (light, string); longitudinal waves vibrate parallel (sound).
Sound is longitudinal and needs a medium — it cannot cross a vacuum.
Amplitude is measured from the rest position to a crest, not trough to crest.
$f = \frac{# cycles}{time} = \frac{1}{T}$ — frequency and period are reciprocals.
$v = f λ$ applies to every wave.
The medium fixes the speed and the source fixes the frequency, so entering a new medium changes the wavelength.
Sound travels fastest in solids, slower in liquids, slowest in gases.

The Speed of Sound, Echoes and Mach Number

$v_{so u n d} = (332 + 0.6 T) m/s$ , with $T$ in degrees Celsius.
Every degree Celsius adds about $0.6 m/s$ ; at $20^{\circ} C$ sound travels $344 m/s$ .
$t_{ec h o} = \frac{2 d}{v}$ — the sound makes a round trip, so the distance travelled is twice the distance to the surface.
Rearranged for distance: $d = \frac{v t _{ec h o}}{2}$ .
$mach # = \frac{v _{o bj ec t}}{v _{so u n d}}$ — a unitless ratio.
Mach less than 1 is subsonic, greater than 1 supersonic, greater than 5 hypersonic.
A sonic boom is produced continuously by a supersonic aircraft, not once at the moment it passes Mach 1.
Doppler: approaching sources sound higher, receding sources sound lower. The emitted frequency never changes.

Reflection, Superposition and Beats

Superposition: where waves overlap, the displacement is the sum of the individual displacements.
A pulse reflecting from a fixed end is inverted; from a free end it is upright.
Constructive interference: waves in phase, displacements add, larger amplitude.
Destructive interference: waves out of phase, displacements cancel, smaller or zero amplitude.
Waves pass through each other unchanged — interference only occurs while they overlap.
$f_{b e a t} = ∣ f_{1} - f_{2} ∣ = \frac{# beats}{time} .$
Zero beats means the frequencies are identical, which is how instruments are tuned.
The absolute value means beats cannot tell you which frequency is higher.

Resonance, Harmonics, Intensity and Hearing

A standing wave has nodes (zero displacement) and antinodes (maximum displacement), with adjacent nodes half a wavelength apart.
Resonance is large-amplitude vibration produced by driving a system at one of its natural frequencies.
Strings and open pipes: $l_{n} = \frac{nλ}{2}$ and $f_{n} = n f_{0}$ — all harmonics.
Closed pipes: $l_{n} = \frac{( 2 n - 1 ) λ}{4}$ and $f_{n} = (2 n - 1) f_{0}$ — odd harmonics only.
A closed pipe sounds one octave lower than an open pipe of the same length.
$\frac{I _{2}}{I _{1}} = \frac{r _{1}^{2}}{r _{2}^{2}}$ and $I \propto \frac{1}{d ^{2}}$ — double the distance, quarter the intensity.
$d B = 10 lo g (\frac{I _{2}}{I _{1}})$ . A tenfold intensity increase is $+ 10 dB$ and sounds about twice as loud.
Hearing damage is permanent, cumulative, and depends on both level and exposure time.

Sound in Technology, Medicine and the Environment

Ultrasound is sound above $20 kHz$ ; medical imaging uses $1$ to $20 MHz$ .
Imaging works by echo timing: $d = \frac{v t _{ec h o}}{2}$ , with $v \approx 1540 m/s$ in soft tissue. The factor of two has not gone away.
The reflectors are the boundaries between tissues, not the organs. Gel excludes the air layer that would otherwise reflect the whole pulse.
Resolution is limited by wavelength and $λ = \frac{v}{f}$ , so higher frequency gives finer detail but is absorbed faster and penetrates less deeply.
An echo is one reflection delayed more than about $0.1 s$ ; reverberation is thousands of early reflections merging into a decaying tail.
Hard surfaces reflect and lengthen reverberation; soft porous surfaces absorb and shorten it. Treatment controls sound inside a room, soundproofing keeps it between rooms.
Ontario workplace noise is capped at $85 dB$ over eight hours, and every $3 dB$ above halves the safe time.
Doubling your distance from a source cuts the intensity to a quarter, about $6 dB$ of protection for free.

Unit 5: Electricity and Magnetism

Static Charge, Current and Electron Flow

Like charges repel, opposite charges attract. Charge is measured in coulombs.
Only electrons move in a solid: gaining them makes an object negative, losing them makes it positive.
Charging happens by friction, contact or induction.
$I = \frac{q}{Δ t}$ — current in amperes, where $1 A = 1 C/s$ .
Conventional current runs positive to negative and is used in every equation and diagram.
Electron flow runs negative to positive and is what physically happens in a metal.
Electron drift velocity is under a millimetre per second; the field, not the electrons, travels near light speed.
Ammeters go in series and have near-zero resistance. Voltmeters go in parallel and have near-infinite resistance.

Voltage, Resistance, Ohm's Law and Electrical Power

A volt is a joule per coulomb: $V$ is the energy given to each unit of charge.
$R = \frac{V}{I}$ , rearranged as $V = I R$ or $I = \frac{V}{R}$ .
An ohmic component has constant resistance and gives a straight line through the origin on a $V$ – $I$ graph.
Resistance rises with length and with temperature, and falls with cross-sectional area.
$P = V I$ — volts times amperes gives watts, because $\frac{J}{C} \times \frac{C}{s} = \frac{J}{s}$ .
$P = I^{2} R$ means power loss grows with the square of the current.
$1 kWh = 3.6 \times 1 0^{6} J$ , and it is a unit of energy, not power.
$E (kWh) = \frac{P (W) \times t (h)}{1000}$ , then multiply by the rate for the cost.

Series and Parallel Circuits

Series: $R_{T} = R_{1} + R_{2} + \dots$ — the total exceeds any individual resistor.
Parallel: $\frac{1}{R _{T}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots$ — the total is less than the smallest resistor.
Remember the final reciprocal in a parallel calculation.
Series: current is the same everywhere; voltages add to the supply.
Parallel: voltage is the same across every branch; currents add to the total.
In series the largest resistor takes the largest voltage; in parallel the smallest resistor takes the largest current.
Two equal resistors in parallel give half of one. For two unequal ones, $R_{T} = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$ .
Houses are wired in parallel so every outlet gets full voltage and devices work independently.

Magnetic Fields, Motors and Transformers

Field lines run from north to south outside a magnet, never cross, and are closest where the field is strongest.
Isolated poles do not exist — cutting a magnet gives two smaller magnets.
Right-hand rules use conventional current: thumb along the current for a straight wire, thumb out of the north pole for a coil.
$F_{M} \propto I$ , $F_{M} \propto n$ , $F_{M} \propto κ$ — an electromagnet is stronger with more current, more turns and a better core.
An electromagnet can be switched off and varied; a permanent magnet cannot.
A current-carrying wire in a magnetic field feels a force perpendicular to both — the motor principle.
Induction requires change: a stationary magnet in a stationary coil induces nothing.
$\frac{N _{1}}{N _{2}} = \frac{V _{1}}{V _{2}} = \frac{I _{2}}{I _{1}}$ — the current ratio is inverted.
Transformers only work on AC, and the grid transmits at high voltage to keep $I^{2} R$ losses low.

Household Circuits, Safety and Static in Practice

A house receives two live conductors and a neutral: $120 V$ from either live to neutral, $240 V$ across both.
Live (black or red) carries current out, neutral (white) carries it back, and ground (bare or green) carries none until a fault occurs.
Branch circuits are wired in parallel so every device gets the full voltage and switches independently; the branch currents add.
A fuse or breaker is a deliberate weak point wired in series, protecting the wiring. A fuse is consumed; a breaker resets.
An overload is too much load on one branch and trips slowly; a short circuit is live touching neutral or ground and trips instantly.
A GFCI compares live and neutral currents and opens on about a $5 mA$ imbalance — it protects people, while a breaker protects wiring.
Current, not voltage, causes harm. $I = \frac{V}{R}$ with dry skin near $100000 Ω$ and wet skin near $1000 Ω$ .
Roughly $100 mA$ through the body causes ventricular fibrillation, while $10$ to $20 mA$ already makes letting go impossible.

Unit 6: Formula Sheet & Exam Reference

How to Attack a Physics Problem

Draw something, list the givens with units, convert to base SI, choose the equation, rearrange, then substitute.
Check four things every time: units, magnitude, direction and sign.
For kinematics, pick the equation missing the variable you neither have nor want.
Multiplying or dividing keeps the fewest significant figures; adding or subtracting keeps the fewest decimal places.
Round only at the end, carrying extra digits through intermediate steps.
Show the substitution line — part marks are awarded for a correct equation and substitution.
Keep the calculator in degree mode for the entire course.
A vector answer without a direction is not a complete answer.